This invention generally relates to a technique to achieve high resolution measurements of petrophysical properties, and more particularly, the invention relates to a technique to generate accurate and high resolution estimates of petrophysical properties by the use of alpha processing.
Nuclear magnetic resonance (NMR) measurements typically are performed to investigate properties of a sample. For example, an NMR wireline or logging while drilling (LWD) downhole tool may be used to measure petrophysical properties that are associated with downhole formations. In this manner, a typical NMR tool may, for example, provide a lithology-independent measurement of the porosity of a particular formation by determining the total amount of hydrogen present in fluids of the formation. Equally important, the NMR tool may also provide measurements that indicate the dynamic properties and environment of the fluids, as these factors may be related to petrophysically important parameters. For example, the NMR measurements may provide permeability and viscosity information that is difficult or impossible to derive from other conventional logging arrangements. Thus, it is the capacity of the NMR tool to perform these measurements that makes it particularly attractive versus other types of downhole tools.
Typical NMR logging tools include a magnet that is used to polarize hydrogen nuclei (protons) in the formation and a transmitter coil, or antenna, that emits radio frequency (RF) pulses. A receiver antenna may measure the response (indicated by received spin echo signals) of the polarized hydrogen to the transmitted pulses. Quite often, the transmitter and receiver antennae are combined into a single transmitter/receiver antenna.
There are several experimental parameters that may be adjusted according to the objectives of the NMR measurement and expected properties of the formation fluids. However, the NMR techniques employed in current NMR tools typically involve some variant of a basic two step sequence that includes a polarization period followed by an acquisition sequence.
During the polarization period (often referred to as a wait time) the protons in the formation polarize in the direction of a static magnetic field (called Bo) that is established by a permanent magnet (of the NMR tool). The growth of nuclear magnetization M(t) (i.e., the growth of the polarization) is characterized by the xe2x80x9clongitudinal relaxation timexe2x80x9d (called T1) of the fluid and its maximum value (called M0), as described by the following equation:       M    ⁢          (      t      )        =            M      0        ⁢          (              1        -                  ⅇ                      -                          t                              T                1                                                        )      
The duration of the polarization period may be specified by the operator (conducting the measurement) and includes the time between the end of one acquisition sequence and the beginning of the next. For a moving tool, the effective polarization period also depends on tool dimensions and logging speed.
Referring to FIG. 1, as an example, a sample (in the volume under investigation) may initially have a longitudinal magnetization MZ 10 of approximately zero. The zero magnetization may be attributable to a preceding acquisition sequence, for example. However, the magnetization MZ 10 (under the influence of the B0 field) increases to a magnetization level (called M(tw (1)) after a polarization time tw (1) after zero magnetization. As shown, after a longer polarization time tw (2) from zero magnetization, the MZ magnetization 10 increases to an M(tw (2)) level.
An acquisition sequence begins after the polarization period. For example, an acquisition sequence may begin at time tw (1), a time at which the magnetization MZ 10 is at the M(tw (1)) level. At this time, RF pulses are transmitted from a transmitter antenna of the tool. The pulses, in turn, produce a train of spin echo signals 16, and the initial amplitudes of the spin echo signals 16 indicate a point on the magnetization MZ 10 curve, such as the M(tw (1)) level, for example. Therefore, by conducting several measurements that have different polarization times, points on the magnetization MZ 10 curve may be derived, and thus, the T1 time for the particular formation may be determined. A receiver antenna (that may be formed from the same coil as the transmitter antenna) receives the train of spin echo signals 16 and stores digital signals that indicate the spin echo signals 16.
As an example, for the acquisition sequence, a typical logging tool may emit a pulse sequence based on the CPMG (Carr-Purcell-Meiboom-Gill) pulse sequence. The application of the CPMG pulse train includes first emitting an RF burst, called an RF pulse, that has the appropriate duration to rotate the magnetization, initially polarized along the B0 field, by 90xc2x0 into a plane perpendicular to the B0 field. The RF pulse that rotates the magnetization by 90xc2x0 is said to introduce a flip angle of 90xc2x0. Next, a train of equally spaced 180xc2x0 RF pulses is transmitted. Each 180xc2x0 RF pulse has the appropriate duration to rotate the magnet moment by 180xc2x0 to refocus the spins to generate each spin echo signal 16. Each RF pulse that rotates the magnetization by 180xc2x0 is said to introduce a flip angle of 180xc2x0. Individual hydrogen nuclei experience randomly time-varying magnetic environments during the pulse sequence, a condition that results in an irreversible loss of magnetization and a consequent decrease in successive echo amplitudes. The rate of loss of magnetization is characterized by a xe2x80x9ctransverse relaxation timexe2x80x9d (called T2) and is depicted by the decaying envelope 12 of FIG. 1.
In general, the above NMR measurement of the T1 time may be referred to as a saturation recovery, or T1-based, measurement due to the fact that the nuclear spins are saturated (i.e., the magnetization is decreased to approximately zero) at the beginning of the wait time. Thus, from the NMR measurement, a value of the magnetization MZ 10 curve may be determined from the initial signal amplitude. In general, an NMR measurement of the signal decay may be labeled a T2-based measurement. It is noted that every T2 measurement is T1 weighted due to the fact that prepolarization occurs during the wait time before the acquisition sequence.
The initial amplitude of the envelope 12 is proportional to the product of the porosity and the hydrogen index of the formation fluids. The rate at which the envelope 12 decays is governed by the chemical nature of the fluids, the fluid viscosity, and the pore structure of the formation, which may be related to permeability. Standard data analysis involves fitting the echo amplitudes to a multi-exponential function. The coefficients which result from the fitting process constitute a relaxation time distribution, usually referred to as a T2 distribution. Small T2 values, deriving from fast relaxing components in the echo train, are generally associated with bound fluid, whereas large T2 values reflect free fluid. Total porosity is proportional to the area under the T2 distribution, which is identical to the initial amplitude of the multi-exponential function. Bound water can be identified with the short T2 components in the distribution, while free fluid generally contributes to the long T2 components.
The precision with which porosity, bound fluid, and free fluid volumes can be derived is determined by the intrinsic noise level of the measurement. In practice, it is usual to average NMR echo data over several depth levels in order to improve the signal-to-noise ratio (SNR) prior to inversion. This procedure improves the accuracy of the computed quantities but degrades the vertical resolution. In thin laminated beds, resolution can be critical for correct petrophysical evaluation, and in these situations, vertical averaging of measurements may be detrimental.
A processing technique for enhancing the vertical resolution of logging data is discussed in U.S. Pat. No. 4,794,792 (the ""792 patent). The ""792 patent discloses using one sensor to obtain an accurate, but low resolution measurement of some property of interest and using another sensor to obtain a less accurate but higher resolution measurement of the property. The ""792 patent also discusses a technique called alpha processing to combine these two measurements to produce an accurate and high-resolution estimate of the property. However, the ""792 patent does not teach generating an accurate, high resolution estimate without the use of multiple sensors: one for the high resolution and low accuracy measurement and another one for the lower resolution and higher accuracy measurement.
NMR log data is customarily processed by applying inversion algorithms to measured echo amplitude decays to yield distributions of transverse relaxation times. The inversion is generally a non-linear operation due to the positivity constraints, which are imposed on the individual populations of the relaxation time distribution. Consequently, both statistical and systematic errors in porosity estimates increase in a non-linear fashion with increasing noise levels. Therefore, to improve the signal-to-noise ratio (SNR) and thus, the accuracy of the data, the echo trains that are collected from different depths may be averaged together. However, this averaging effectively degrades the resolution provided by these echo trains.
A technique for more efficiently inverting NMR echo data using window-sums is disclosed in U.S. Pat. No. 5,291,137. This algorithm is described for non-linear inversion of data acquired at a single depth or for depth-averaged data.
Thus, there is a continuing need for a technique that addresses one or more of the problems that are stated above.